Question:
The ratio of radii of first orbits of He\(^+ \) and Li\(^{2+}\) is:
The ratio of radii of first orbits of He\(^+ \) and Li\(^{2+}\) is:
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Key Fact: In hydrogen-like atoms, the radius of an orbit is inversely proportional to the atomic number \( Z \).
Updated On: May 27, 2025
- 2:3
- 3:2
- 1:2
- 4:3
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The Correct Option is B
Solution and Explanation
Step 1: Use the Radius Formula for Hydrogen-like Atoms
The radius of the first orbit (\( n = 1 \)) is given by: \[ r \propto \frac{n^2}{Z} \] For \( n = 1 \): \[ r \propto \frac{1}{Z} \]
Step 2: Calculate for He\(^+ \)
For He\(^+ \), \( Z = 2 \), \( n = 1 \): \[ r_{\text{He}^+} \propto \frac{1}{2} = 0.5 \]
Step 3: Calculate for Li\(^{2+} \)
For Li\(^{2+} \), \( Z = 3 \), \( n = 1 \): \[ r_{\text{Li}^{2+}} \propto \frac{1}{3} \approx 0.333 \]
Step 4: Find the Ratio
\[ \text{Ratio} = \frac{r_{\text{He}^+}}{r_{\text{Li}^{2+}}} = \frac{0.5}{0.333} = \frac{3}{2} \]
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